To solve these questions, we need to calculate the interest accrued during the deferment period and the monthly payment on the loan after Angelica begins repayment.

Part 1: Interest Accrued During Deferment

The formula for the future value of a loan under compound interest is:

$A = P \times (1 + \frac{r}{n})^{n \cdot t}$

Where:

• $A$ = future value of the loan after deferment (including accrued interest)
• $P$ = principal amount of the loan ($11,000)
• $r$ = annual interest rate (5.2% or 0.052)
• $n$ = number of times interest is compounded per year (12 for monthly compounding)
• $t$ = time in years (4 years of deferment)

Step 1: Plug in the values

$A = 11,000 \times (1 + \frac{0.052}{12})^{12 \cdot 4}$

$A = 11,000 \times (1 + 0.0043333)^{48}$

Step 2: Calculate the result

$A \approx 11,000 \times 1.221677$

$A \approx 13,438.45$

The total loan balance after 4 years of deferment is approximately $13,438.45. The interest accrued is:

$\text{Interest} = A - P$

$\text{Interest} \approx 13,438.45 - 11,000 = 2,438.45$

Thus, the interest accrued during the deferment period is $2,438.45.

---

Part 2: Monthly Payment Calculation

The formula for monthly payment under an amortized loan is:

$M = P \times \frac{r/n}{1 - (1 + r/n)^{-n \cdot t}}$

Where:

• $M$ = monthly payment
• $P$ = loan balance at the start of repayment ($13,438.45, including accrued interest)
• $r$ = annual interest rate (0.052)
• $n$ = number of payments per year (12)
• $t$ = time in years (12 years after deferment)

Step 1: Plug in the values

$M = 13,438.45 \times \frac{0.052/12}{1 - (1 + 0.052/12)^{-12 \cdot 12}}$

$M = 13,438.45 \times \frac{0.0043333}{1 - (1 + 0.0043333)^{-144}}$

Step 2: Calculate the result

1. Calculate the denominator: $1 - (1 + 0.0043333)^{-144} \approx 1 - 0.5574 \approx 0.4426$

2. Calculate the numerator: $0.0043333 / 0.4426 \approx 0.009791$

3. Calculate $M$: $M \approx 13,438.45 \times 0.009791 \approx 131.49$

Thus, the monthly payment is $131.49.

---

Final Answers:

1. Interest accrued during deferment: $2,438.45
2. Monthly payment: $131.49

Would you like to see a step-by-step explanation of the formulas or calculations?

Related Questions:

1. How would the results change if the interest rate were higher, say 6%?
2. What is the total amount Angelica will pay over the life of the loan?
3. How much principal is paid versus interest in the first year of repayment?
4. How long would it take to pay off the loan if Angelica increased her monthly payment by $50?
5. What would be the monthly payment if she paid off the loan in 8 years instead of 12?

Tip:

When calculating compound interest, remember to adjust the formula for the compounding frequency (e.g., monthly, quarterly, annually) to get precise results.